If I generate some data using
data = RandomVariate[NormalDistribution[5, 3], 100]
Then find the distribution using
Mathematica gives me an estimated distribution (correctly guesses a Normal) and values of that distributions parameters.
However, if I then do
EstimatedDistribution[data, NormalDistribution[a, b]]
FindDistributionParameters[data, NormalDistribution[a, b]]
Mathematica gives me different "best fit" parameter estimates. Using defaults, (2) and (3) give the same results, and (1) gives different results.
Looking at the documentation it looks like (2) and (3) might use a different method by default to (1). But I have been unable to get (1) to give the same results as (2) and (3). Is there a simple way (options) to make the results consistent.
A couple of more general questions:
Are there any "rules" as to when one should use (1), versus (2) or (3) to get parameter values. Obviously (1) finds a distribution, versus (2) and (3) finding best fit parameters of a specified distribution.
The three functions seem very related, so it seems confusing that by default they did not give the same best fit parameters.